\(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory

DOI10.1007/s11785-020-01042-xzbMath1486.44007OpenAlexW3120352462MaRDI QIDQ2027976

Hatem Mejjaoli

Publication date: 28 May 2021

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-020-01042-x

zbMATH Keywords

extremal functionsreproducing kernelTikhonov regularizationMoore-Penrose inversetime-frequency concentrationgeneralized Sobolev spaces\(k\)-Hankel Gabor transform

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Integral transforms of special functions (44A20) Integral operators (47G10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Pseudodifferential operators (47G30)

Related Items

Time-frequency analysis associated with the deformed Stockwell transform ⋮ \(k\)-Hankel Wigner transform and its applications to the localization operators theory ⋮ \(L^p\) boundedness and compactness of localization operators associated with the \(k\)-Hankel wavelet transform on \({\mathbb{R}}^d \) ⋮ Linear canonical deformed Hankel transform and the associated uncertainty principles ⋮ Localization operators and scalogram associated with the deformed Hankel wavelet transform ⋮ Time-frequency analysis of (k,a)-generalized wavelet transform and applications ⋮ Generalized translation operator and uncertainty principles associated with the deformed Stockwell transform ⋮ Generalized convolution operator associated with the \((k, a)\)-generalized Fourier transform on the real line and applications ⋮ Some uncertainty inequalities for the continuous wavelet transform ⋮ Time-frequency analysis associated with the \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) ⋮ Toeplitz operators associated with the deformed windowed Fourier transform

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• General inhomogeneous discrete linear partial differential equations with constant coefficients on the whole spaces
• An alternative description of Gabor spaces and Gabor-Toeplitz operators
• Uncertainty principles for the Dunkl transform
• Explicit formulas for the Dunkl dihedral kernel and the \((\kappa,a)\)-generalized Fourier kernel
• Wavelet transforms and localization operators
• Heisenberg inequalities for Jacobi transforms
• Annihilating sets for the short time Fourier transform
• On Fourier transforms of functions supported on sets of finite Lebesgue measure
• The uncertainty principle: A mathematical survey
• Continuous Gabor transform for strong hypergroups
• Time-frequency analysis of localization operators.
• Foundations of time-frequency analysis
• Localization type Berezin-Toeplitz operators on bounded symmetric domains.
• Spectral theorems associated with the \((k,a)\)-generalized wavelet multipliers
• Localization operators and an uncertainty principle for the discrete short time Fourier transform
• A product formula and a convolution structure for a \(k\)-Hankel transform on \(\mathbb{R}\)
• Positivity of Dunkl's intertwining operator
• New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform
• \((k,a)\)-generalized wavelet transform and applications
• Translation operator and maximal function for the \((k,1)\)-generalized Fourier transform
• Strichartz estimates for Schrödinger-Laguerre operators
• Uncertainty principles for the continuous Dunkl Gabor transform and the Dunkl continuous wavelet transform
• Commutative algebras of Toeplitz operators on the Bergman space
• Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.)
• On accumulated spectrograms
• Weighted inequalities and uncertainty principles for the (k,a)-generalized Fourier transform
• An Excursion into Berezin–Toeplitz Quantization and Related Topics
• Heisenberg uncertainty inequality for Gabor transform
• Dunkl operators and a family of realizations of $\mathfrak{osp}(1\vert2)$
• QUALITATIVE UNCERTAINTY PRINCIPLE FOR GABOR TRANSFORM
• Uncertainty Principles and Signal Recovery
• The Schrödinger model for the minimal representation of the indefinite orthogonal group 𝑂(𝑝,𝑞)
• Time-Frequency Localization via the Weyl Correspondence
• Laguerre semigroup and Dunkl operators
• UNIFORM EIGENVALUE ESTIMATES FOR TIME-FREQUENCY LOCALIZATION OPERATORS
• Toeplitz operators and localization operators
• Some comments on Fourier analysis, uncertainty and modeling
• Differential-Difference Operators Associated to Reflection Groups
• Time-frequency localization operators: a geometric phase space approach
• The wavelet transform, time-frequency localization and signal analysis
• Anti-Wick quantization with symbols in $L^p$ spaces
• Pitt's Inequalities and Uncertainty Principle for Generalized Fourier Transform
• k-Hankel two-wavelet theory and localization operators
• Dunkl-Gabor transform and time-frequency concentration
• Heisenberg-type inequalities for the Weinstein operator
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I
• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions
• WICK AND ANTI-WICK OPERATOR SYMBOLS
• Theory of Reproducing Kernels